The book under review was commissioned by the International Mathematical Union in celebration of World Mathematical Year 2000. It contains essays by some of the leading lights in mathematics today. The reviewer notes that the book is not an easy read and that the average reader will gain most by choosing some chapters for careful study and skimming the remaining material. The book discusses such areas as mathematical physics, discrete mathematics, number theory, topology, and applied mathematics. However, the reviewer notes, the field of theoretical computer science is missing from the volume. Nevertheless, he writes, "This collection demonstrates well that mathematics is alive and vital."